Resonant frequency and circumference of spheres

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Discussion Overview

The discussion revolves around the resonant frequency of hollow spherical objects, particularly in the context of electromagnetic and acoustic waves. Participants explore the relationship between resonant frequencies, wavelengths, and the circumference of spheres, as well as the implications of Schumann resonances related to the Earth.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions whether the resonant frequency of a hollow spherical object can equal its circumference, prompting a discussion about the nature of frequency and distance.
  • Another participant clarifies that a circumference is a distance and a resonant frequency is a frequency, suggesting that equating the two does not make sense.
  • A participant later refines their question to inquire if wavelength or its inverse can equal the circumference of a spherical object.
  • Suggestions are made to explore the concept of whispering gallery resonators, which are not spherical but cylindrical.
  • One participant presents a formula for sphere resonance, f = v / (2*pi*r), and seeks validation of its correctness.
  • Schumann resonances are introduced as resonant modes within a spherical shell, with references to external sources for further reading.
  • A participant discusses Mie scattering in relation to electromagnetic resonances and notes that resonances begin when ka = 1, where ka is the circumference measured in wavelengths.
  • Another participant raises a question about the factors influencing Schumann resonance frequencies, including the ionosphere and the Earth's molten core, and proposes a modified equation to account for these factors.
  • Discussion includes the conductivity of the Earth's surface and its implications for Schumann resonances, with one participant expressing skepticism about the relevance of the molten core.
  • A later reply acknowledges the variability of Schumann resonances due to changes in the ionosphere, noting a small discrepancy in frequency values.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between resonant frequencies and the circumference of spheres, with no consensus reached on the initial question. The discussion on Schumann resonances also reveals varying interpretations of contributing factors, indicating multiple competing views.

Contextual Notes

Limitations include the dependence on definitions of resonant frequency and wavelength, as well as unresolved mathematical steps in the proposed equations. The discussion also highlights the complexity of factors influencing Schumann resonances.

Who May Find This Useful

Individuals interested in the physics of resonant frequencies, wave phenomena, and the properties of spherical objects, as well as those studying Earth sciences and electromagnetic theory.

nuby
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Does the electromagnetic or acoustic resonant frequency of a hallow spherical object ever equal the circumference of that object? If not what are the formulas to calculate this? Thanks in advance.
 
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A circumference is a distance. A resonant frequency is a frequency. Talking about a distance being equal to a frequency doesn't make sense; it's like asking if your age equals your name.
 
True... I think I asked the wrong question..
Anyway, do you know the equation to calculate the resonant frequency of a hollow sphere, and string?

Thanks.
 
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I meant to ask if wavelength or 1/wavelength is ever equal to the circumference of an spherical object.
 
In which context?
I suggest you google "whispering gallery resonator",although they are no spherical but cylindrical.
 
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Does this look right for sphere resonance?

f = v / (2*pi*r)
 
The previous post described EM resonances internal to a conducting sphere. The complementary exterior problem results in scattering of EM waves off of a conducting sphere. This is known as Mie scattering and the solutions and equations are not simple (the scattered waves are combinations of reflections from the front with resonant "creeping waves" that travel over the spherical surface). However resonances begin when [tex]ka = 1[/tex], where [tex]ka[/tex] is the circumference of the sphere measured in wavelengths.

You can find the mathematical details in Jackson, Classical Electrodynamics, 2nd ed., section 9.13. The plot of how the scattering amplitude changes with circumference is found in every discussion of radar scattering cross section. See, e.g., Fig. 7 in
http://www.tscm.com/rcs.pdf"
 
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  • #10
A little off topic, but ...
Does the Schumann resonance have more to do with the ionosphere or the molten iron within the earth? According to Wiki, it has to do with the ionosphere and Earth's surface. But why is this:

Schumann resonance equation: c/(2*pi*earth_radius) * sqrt(n*(n+1))

Which comes out to be 7.49 hz ..

switch: earth_radius to earth_radius + ionosphere_elevation .. you get 7.15 hzBut the real Schumann frequency is 7.8 hz ...

Since the upper mantel depth is right around 250,000 meters

Wouldn't c/(2*pi*(earth_radius - upper_mantel_depth)) make sense?
So you get the real Schumann frequency of 7.8hz?
 
  • #11
The Earth's surface looks like a good conductor when viewed on a large scale. Ground is used as the return conductor for AC power transmission, for instance. The wavelength at 7 Hz = 37000 km, so underground water tables contribute to the apparent conductivity, and any local surface features are irrelevant. The Earth is largely covered with conductive oceans, furthermore. I doubt that you need to consider the molten core.
EDIT: I just noticed you are talking about a depth of just 250 km. I suppose there might be some penetration that deep, although I still think the crust and water tables are quite conductive.
 
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  • #12
Had a chance to look into Schumann resonances a little. Jackson points out that, of the two boundaries, it is the ionosphere that departs most from a perfect conductor and as a result the resonances vary with daily changes in the ionosphere.

Given these factors, your agreement (7.5 vs. 7.8 Hz, or within 4%) is excellent.
 

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